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Explore the mathematical concepts of relative Satake isomorphism and Euler systems in this 55-minute conference talk delivered at the International Centre for Theoretical Sciences. Delve into advanced number theory topics as part of the "Automorphic Forms and the Bloch–Kato Conjecture" program, which examines recent developments and connections between automorphic forms and the arithmetic of special values of L-functions. Learn about the central problem in number theory concerning the arithmetic nature of special values of complex L-functions associated with algebraic varieties, motives, or automorphic representations over global fields, and discover how these L-values connect to the orders of associated algebraic structures such as Chow groups or Selmer groups. Gain insights into how automorphic forms serve as essential tools for studying L-values and understand their foundational role in recent mathematical progress, including generalizations of the Birch and Swinnerton-Dyer conjecture through the Bloch-Kato conjecture framework.
